Concepts and features
R&S
®
ZNB/ZNBT
129
User Manual 1173.9163.02 ─ 62
●
Renormalization of the balanced port impedances affects all measured quantities
that the analyzer provides for balanced ports.
The default reference impedance of a physical port is equal to the reference impe-
dance of the connector type assigned to the port (50 Ω or 75 Ω). It can be defined as a
complex value. For balanced ports, it is possible to define separate complex reference
impedances for differential and for common mode.
The default values for the balanced port reference impedances are derived from the
default reference impedance of the physical analyzer ports (Z
0
= 50 Ω):
●
The default value for the differential mode is Z
0d
= 100 Ω = 2*Z
0
.
●
The default value for the common mode is Z
0c
= 25 Ω = Z
0
/2
Renormalization can be based on two alternative waveguide circuit theories whose
conversion formulas may yield different results if the reference impedance of at least
one test port has a non-zero imaginary part.
Conversion formula for wave quantities and S-parameters
Renormalization transforms the "raw" S-matrix S
0
for the default reference impedances
Z
0i
(with physical port number index i = 1,2,...,n) into a "renormalized" S-matrix S
1
for
the modified reference impedances Z
1i
. In terms of raw and renormalized wave quanti-
ties a
0i
, b
0i
and a
1i
, b
1i
, S
0
and S
1
are defined as follows:
.
...
...
;
...
...
1
12
11
1
1
12
11
0
02
01
0
0
02
01
n
n
n
n
a
a
a
S
b
b
b
a
a
a
S
b
b
b
The renormalized wave quantities (a
1
and b
1
) and the S-matrix S
1
can be calculated
from S
0
and the reference impedances Z
0i
, Z
1i
according to two alternative waveguide
circuit theories.
1.
Traveling waves
In the model of Marks and Williams ("A General Waveguide Circuit Theory"), the
wave quantities a and b are transformed as follows:
i
i
i
i
i
i
i
i
i
i
i
i
i
i
i
i
i
b
a
Z
Z
Z
Z
Z
Z
Z
Z
Z
Z
Z
Z
Z
b
a
0
0
1
0
1
0
1
0
1
0
0
1
1
0
0
1
1
)
Re(
)
Re(
2
1
The renormalized S-matrix S1 is calculated as:
P
S
E
S
P
S
1
0
0
1
1
with the unit matrix E and two additional matrices with the elements
i
i
i
i
ii
Z
Z
Z
Z
0
1
0
1
Measurement results
